No, you can not delete the primary admistrator account.
You can rename it if you like though.
EDIT: Just for clarification - you can make the admistator account your own. I'm not sure how you do that in XP home though as I'm pretty sure you have to create an account when you setup Windows.
Honestly though, having a spare admistrator account is a really good idea so long as you make the password secure. It's handy if you're having a problem with your profile and need to test with another admin level account.